Positive 1D and 2D Systems (Communications and Control Engineering) - Tapa dura

Kaczorek, Tadeusz

 
9781852335083: Positive 1D and 2D Systems (Communications and Control Engineering)
Tapa dura
ISBN 10: 1852335084 ISBN 13: 9781852335083
Editorial: Springer, 2001

Sinopsis

1. Positive matrices and graphs.- 1.1 Generalised permutation matrix, nonnegative matrix, positive and strictly positive matrices.- 1.2 Reducible and irreducible matrices.- 1.3 The Collatz - Wielandt function.- 1.4 Maximum eigenvalue of a nonnegative matrix.- 1.5 Bounds on the maximal eigenvalue and eigenvector of a positive matrix.- 1.6 Dominating positive matrices of complex matrices.- 1.7 Oscillatory and primitive matrices.- 1.8 The canonical Frobenius form of a cyclic matrix.- 1.9 Metzler matrix.- 1.10 M-matrices.- 1.11 Totally nonnegative (positive) matrices.- 1.12 Graphs of positive systems.- 1.13 Graphs of reducible, irreducible, cyclic and primitive systems.- Problems.- References.- 2. Continuous-ime and discrete-ime positive systems.- 2.1 Externally positive systems.- 2.1.1 continuous-time systems.- 2.1.2 discrete-time system.- 2.2 Internally positive systemst.- 2.2.1 continuous-time systems.- 2.2.2 discrete-time systems.- 2.3 Compartmental systems.- 2.3.1 continuous-time systems.- 2.3.2 discrete-time systems.- 2.4 Stability of positive systems.- 2.4.1 Asymptotic stability of continuous-time systems.- 2.4.2 Asymptotic stability of discrete-time systems.- 2.5 Input-output stability.- 2.5.1 BIBO stability of positive continuous-time systems.- 2.5.2 BIBO stability of internally positive discrete-time systems.- 2.6 Weakly positive systems.- 2.6.1 Weakly positive continuous-time systems.- 2.6.2 Equivalent standard systems for singular systems.- 2.6.3 Reduction of weakly positive systems to their standard forms.- 2.6.4 Weakly positive discrete-time systems.- 2.6.5 Reduction of weakly positive systems to standard positive systems.- 2.7 Componentwise asymptotic stability and exponental stability of positive systems.- 2.7.1 continuous-time systems.- 2.7.2 discrete-time systems.- 2.8 Externally and internally positive singular systems.- 2.8.1 continuous-time systems.- 2.8.2 discrete-time systems.- 2.9 Composite positive linear systems.- 2.9.1 Discrete-ime systems.- 2.9.2 continuous-time systems.- 2.10 Eigenvalue assignment problem for positive linear systems.- 2.10.1 Problem formulation.- 2.10.2 Problem solution.- 2.11.2 Positive systems with nonnegative feedbacks.- Problems.- References.- 3. Reachability, controllability and observability of positive systems.- 3.1 discrete-time systems.- 3.1.1 Basic definitions and cone of reachable states.- 3.1.2 Necessary and sufficient conditions of the reachability of positive systems.- 3.1.3 Application of graphs to testing the reachability of positive systems.- 3.2 continuous-time systems.- 3.2.1 Basic definitions and reachability cone.- 3.3 Controllability of positive systems.- 3.3.1 Basic definitions and tests of controllability of discrete-time systems.- 3.3.2 Basic definitions and controllability tests of continuous-time systems.- 3.4 Minimum energy control of positive systems.- 3.4.1 discrete-time systems.- 3.4.2 continuous-time systems.- 3.5 Reachability and controllability of weakly positive systems with state feedbacks.- 3.5.1 Reachability.- 3.5.2 Controllability.- 3.6 Observability of discrete-time positive systems.- 3.6.1 Cone of positive initial conditions.- 3.6.2 Necessary and sufficient conditions of observability.- 3.6.3 Dual positive systems and relationships between reachability and observability.- 3.7 Reachability and controllability of weakly positive systems.- 3.7.1 Reachability.- 3.7.2 Controllability.- Problems.- References.- 4. Realisation problem of positive 1D systems.- 4.1 Basic notions and formulation of realisation problem.- 4.1.1 Standard discrete-time systems.- 4.1.2 Standard continuous-time systems.- 4.2 Existence and computation of positive realisations.- 4.2.1 Computation of matrix D of a given proper rational matrix.- 4.2.2 Existence and computation of positive realisations of discrete-time single-input single-output systems.- 4.2.3 Existence and computation of positive realisations of continuous-time single-input single-output systems.- 4.2.4 Necessar...

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Reseña del editor

The presence of uncertainty in a system description has always been a critical issue in control. Moving on from earlier stochastic and robust control paradigms, the main objective of this book is to introduce the reader to the fundamentals of probabilistic methods in the analysis and design of uncertain systems. Using so-called randomized algorithms, this emerging area of research guarantees a reduction in the computational complexity of classical robust control algorithms and in the conservativeness of methods like H¥ control. Features: · self-contained treatment explaining the genesis of randomized algorithms in the principles of probability theory to their use for robust analysis and controller synthesis; · comprehensive treatment of sample generation, including consideration of the difficulties involved in obtaining identically and independently distributed samples; · applications of randomized algorithms in congestion control of high-speed communications networks and the stability of quantized sampled-data systems. Randomized Algorithms for Analysis and Control of Uncertain Systems will be of certain interest to control theorists concerned with robust and optimal control techniques and to all control engineers dealing with system uncertainties.

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Editorial
Springer
Año de publicación
2001
Idioma
Inglés
ISBN 10 
1852335084
ISBN 13 
9781852335083
Encuadernación
Tapa dura
Número de páginas
448
Contacto del fabricante
Springer Nature Customer Service Center GmbH
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Europaplatz 3,69115 Heidelberg, Germany
Heidelberg
69115
Alemania

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9781447110972: Positive 1D and 2D Systems (Communications and Control Engineering)

Edición Destacada

ISBN 10:  1447110978 ISBN 13:  9781447110972
Editorial: Springer, 2012
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